Indeed, Gurren-Lagann only used the Super Robot clichés superficially. The real themes behind the action and plot can't really be called "generic". The show is akin to a good Pixar movies: as mature as it is childish.
Let's take the Anti-Spirals. One can't completely write off them as simplistic bad guys, as we're offered from them an interesting, if brief, commentary on carbon-based life. It was probably brief because it's depressing to contemplate the big picture. Spirals are viewed as this grave threat to the universe because life does what life does: consumes and multiplies without consideration. It thus fell to the Anti-Spirals to put carbon-based life in its place, which is to say, in convenient and easy to manage boxes, with the threat of complete extermination to keep them from expanding outside of their boundaries. Eventually, in theory, the molten crust of the respective planets would cool, and they'd all die anyway, causing minimal additional damage to the cold and austere beauty of the universe.
It's a situation that plays out all the time, with humans in the role of Anti-Spirals, and weeds, pests, and even other humans in the role of Spirals. Trying to stem the vicious rampancy of growth and consumption sounds like a just and responsible thing to do, especially when described with terms like vicious and rampant, until the realization hits that doing so may involve some messy details, like inducing resource starvation or just plain death.